Calculator Servicescalculatorservices.com
Geometry

Equilateral Triangles

Equilateral triangle formulas. Free online Equilateral Triangles. Calculate equilateral triangles online — fast, accurate, mobile-friendly, no signup needed.

All three sides and angles are equal (60°).
Area
15.588457
Height
5.196152
Perimeter
18

Derivation

  1. ├── 01Givens = 6
  2. ├── 02FormulaArea: √(3) / 4 × t²
  3. ├── 03Compute Area15.588457
  4. ├── 04FormulaHeight: √(3) / 2 × t
  5. ├── 05Compute Height5.196152
  6. ├── 06FormulaPerimeter: 3 × e.s
  7. ├── 07Substitute3 × e.6
  8. └── 08Compute Perimeter18
Did you know?

Pythagoras of Samos (c. 570–495 BCE) likely wasn’t the first to find a²+b²=c² — Babylonian tablets from ~1800 BCE used it — but the first rigorous proof is credited to his school.

§01What is

Understanding the Equilateral Triangles

The Equilateral Triangles computes Area from 1 input: side length. Equilateral triangle formulas.

Geometry is what turns raw measurements into useful answers about space — how much paint, how big a yard, how much material a project will need. Every craftsperson, architect, and DIYer reaches for these formulas regularly. The Equilateral Triangles sits in that toolkit — it equilateral triangle formulas. Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.

§02The Formula

How it’s calculated

Area = √(3) / 4 × t² | Height = √(3) / 2 × t | Perimeter = 3 × e.s

Where

s
Side length
Area
Output value
Height
Output value
Perimeter
Output value
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: Side length = 6.

  1. 01Start by noting the input — Side length: 6.
  2. 02Substitute these values into the formula: Area = √(3) / 4 × t² | Height = √(3) / 2 × t | Perimeter = 3 × e.s
  3. 03Compute Area: the calculator returns 15.5885.
  4. 04Compute Height: the calculator returns 5.19615.
  5. 05Compute Perimeter: the calculator returns 18.
  6. 06Cross-check the answer by opening the Derivation panel above — every line of math is shown so you can follow the computation end-to-end.
§04Variants

Common Equilateral Triangles Problems

The formula gets rearranged depending on which variable you need. Here are the patterns you’ll run into in the real world — find the one that matches your problem and follow the worked steps.

01 · PATTERN

Side length halved

s = 3 (from 6)

Keep every other input at its default and halve the side length. See how area responds.

  1. 01New Side length: 3
  2. 02Baseline Area: 15.5885
  3. 03New Area: 3.89711
  4. 04Area decreases by 75% → use this sensitivity to plan for real-world variation.
02 · PATTERN

Side length doubled

s = 12 (from 6)

Keep every other input at its default and double the side length. See how area responds.

  1. 01New Side length: 12
  2. 02Baseline Area: 15.5885
  3. 03New Area: 62.3538
  4. 04Area increases by 300% → use this sensitivity to plan for real-world variation.
§05FAQ

Frequently asked questions

Yes. The calculator implements the standard formula as documented and returns exact floating-point results. No approximations are used unless noted in the formula.
Your feedback

How useful was this calculator?

Your ratings stay in your browser — they help us learn which tools people actually rely on.

Rate it
Was this helpful?